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(1)

\

T

p

[49]

(2)

i=1

i

i

i∈N

i

i+1

∞ n=1

−n

kxk≤n

kxk≤n

t→∞

ε>0

K⋐T

t∈T \K

\

K

1

1

1

1

1

1

1

(3)

1

1

1

1

1

1

1

1

1

0

0

n

n

n

n

0

n

n

n

n

n

n

0

n

nk

0

0

nk

0

0

nk

nk

nk

k

nk

nk

0

0

nk

nk

nk

0

nk

nk

ti

ki=1t

1

p

sij

j

ki=1sjpj=1

j

j

sij

sij

j

j

sij

j

sij

j

j

j

t→∞

kxk≤M

(4)

K,M

kxk≤M,t∈K

K,M

o

o

K

o

0

n

n

n

n

n

n

n

n

n

0

nk

nk

n

n

0

1

l

1

l

o

t→∞

\

T

(5)

t∈T

T

T

K⋐T

t→∞

T

K

ε>0

K⋐T

K⋐T

t∈K

T

T \K

t→∞

kxk≤M

t∈T

T

T

T

T

o

o

o

0

0

0

T

T \K

0

\

K

0

t0

0

t0

1

p

0

1

0

p

0

0

j

\

K

0

j

\

T \K

0

(6)

\

T \K

1

1

1

1

\

K

1

\

T \K

1

T

K

\

K

\

T \K

kxk→∞

t∈T

t∈T

T

T

kxk≤M, t∈T

(7)

t∈T

\

{s:kx(s)k≤M }

\

{s:kx(s)k>M }

t∈T

\

{s:kx(s)k≤M }

\

{s:kx(s)k>M }

t∈T

\

T

T

T −T

k−1

\

0

|x|→∞

t∈[0,∞)

\

−∞

(8)

t→∞

kxk→∞

k+

1

k

k

k

\

Rk

+

k+

k

|x|→∞

t∈[0,∞)

\

Rk

k+

t→∞

|x|→∞

′′

∂t2G2

s→t

∂G

∂t

s→t+ ∂G∂t

\

−∞

(9)

′′

t\

−∞

\

t

\

−∞

2

2

s→t

s→t+

−1/2

\

Γ

−1/2

−1

1/2

\

Γ

1/2

−1

1/2

\

Γ

1/2

−1

−1/2

1/2

2

2

1/2

1/2

1/2

−v|t−s|

s→t

s→t+

s→t

12

−1/2

1/2

s→t+

12

−1/2

1/2

(10)

s→t 1

2

1/2

s→t+

12

1/2

12

12

|t|→∞

kxk→∞

t→∞

kxk≤M

t→∞

kxk≤M

kxk≤M

t→∞

t∈R

\

−∞

t∈R

t\

−∞

−v(t−s)

\

t

−v(s−t)

kxk→∞

t∈T

kxk→∞

0

0

(11)

′′

0

0

12

−1/2

1/2

0

1/2

1

−v(t+s−2t0)

2

−w|t−s|

1

2

\

t0

0

|t|→∞

0

kxk→∞

1

2

t∈[t0,∞)

\

t0

t∈[t0,∞)

\

t0

1

−v(t+s−2t0)

2

−w|t−s|

t∈[t0,∞)

1

−v(t+s−2t0)

s=t0

2

−w(t−s)

ts=t0

2

−w(s−t)

s=t

t∈[t0,∞)

1

−v(t−t0)

2

2

−w(t−t0)

2

1

2

(12)

kxk→∞

t∈T

kxk→∞

1

2

## v < 1 L . Then from Theorem 4 we obtain the assertion.

### R´evis´e le 17.11.1997 et le 25.3.1998

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